SAT Math: Quadratic Equations Flashcards

Question 1

Define Standard Form of a Quadratic.

Accepted Answer

The arrangement y = ax² + bx + c with a not equal to zero; it shows the y-intercept c directly and feeds straight into the quadratic formula.

Question 2

Define Vertex Form.

Accepted Answer

Writing a quadratic as y = a(x − h)² + k; read h and k straight off the brackets to get the parabola's turning point (h, k), no algebra needed.

Question 3

Define Factored Form.

Accepted Answer

Writing a quadratic as y = a(x − p)(x − q); each bracket set to zero gives one zero of the parabola, so p and q are read off directly.

Question 4

Define Leading Coefficient a.

Accepted Answer

The number multiplying x²; a positive value makes the parabola open upward, a negative value makes it open downward, and a larger size narrows it.

Question 5

What is Parabola?

Accepted Answer

The symmetric U-shaped curve produced by graphing any quadratic function, either cupped upward or turned downward.

Question 6

Define Turning Point (Vertex).

Accepted Answer

The single point where a parabola changes direction, giving the lowest value of an upward curve or the highest value of a downward curve.

Question 7

Define Vertex Formula x = −b/(2a).

Accepted Answer

A shortcut that gives the horizontal position of a parabola's turning point straight from standard form, without completing the square.

Question 8

Define Axis of Symmetry.

Accepted Answer

The vertical line through a parabola's turning point that splits the curve into two mirror-image halves; it lies midway between the x-intercepts.

Question 9

Define Zero Product Property.

Accepted Answer

If a product of factors equals zero, at least one of those factors must equal zero, which turns a factored equation into simple linear ones.

Question 10

Define Quadratic Formula.

Accepted Answer

x = (−b ± √(b² − 4ac)) ÷ 2a solves any equation ax² + bx + c = 0, including ones that do not factor neatly.

Question 11

What is Discriminant?

Accepted Answer

The value b² − 4ac under the square root in the quadratic formula; its sign tells how many real solutions an equation has before solving it.

Question 12

Define Positive Discriminant.

Accepted Answer

When b² − 4ac is greater than zero, the equation has two different real solutions and its graph cuts the x-axis twice.

Question 13

Define Double Root.

Accepted Answer

When b² − 4ac equals zero, both solutions coincide in one repeated value and the parabola just touches the x-axis at its turning point.

Question 14

Define No Real Solutions.

Accepted Answer

When b² − 4ac is below zero, the formula would need the square root of a negative number, so the graph never reaches the x-axis.

Question 15

Define Sum of the Roots Shortcut.

Accepted Answer

Without solving anything, the two roots of any quadratic ax² + bx + c = 0 total negative b divided by a, turning a sum question into one division.

Question 16

Define Product of the Roots Shortcut.

Accepted Answer

Without solving anything, the roots of a quadratic in standard form multiply to the constant term c divided by the leading coefficient a.

Question 17

Define Completing the Square.

Accepted Answer

Rewriting x² + bx by adding (b/2)², which turns it into the perfect square (x + b/2)²; it is how standard form is converted to vertex form.

Question 18

Define Difference of Squares.

Accepted Answer

The pattern a² − b² = (a − b)(a + b), which factors any expression made of one perfect square subtracted from another.

Question 19

Define Perfect Square Trinomial.

Accepted Answer

A three-term expression of the form a² ± 2ab + b², which collapses into (a ± b)²; its middle term is twice the product of the square roots.

Question 20

Define Greatest Common Factor First.

Accepted Answer

Before any other method, pull out the largest number or variable shared by every term; it often leaves a simpler expression to factor.

Question 21

Define AC Method for Factoring.

Accepted Answer

To factor ax² + bx + c, find two numbers that multiply to a·c and add to b, then split the middle term and factor by grouping.

Question 22

Define Square Root Method.

Accepted Answer

When an equation has the form (x + p)² = q, take the square root of both sides, remembering both the positive and negative root.

Question 23

Define Constant Term as y-Intercept.

Accepted Answer

In standard form the lone number c is where the parabola meets the vertical axis, since every x term vanishes when x equals zero.

Question 24

Define Projectile Height Model.

Accepted Answer

h(t) = −16t² + v₀t + h₀ gives a launched object's height in feet after t seconds, where v₀ is launch speed and h₀ the starting height.

Question 25

Define Linear–Quadratic System.

Accepted Answer

A line paired with a parabola; substituting the line into the quadratic gives one equation whose solutions are the crossing points, of which there can be zero, one or two.

Question 26

Define Maximum or Minimum Value.

Accepted Answer

The y-coordinate of the turning point: the greatest output of a downward parabola or the least output of an upward one.

Question 27

Define Choosing an Equivalent Form.

Accepted Answer

Standard, vertex and factored forms describe the same parabola; the SAT often asks which form reveals a feature, such as the minimum or the zeros, as a constant or coefficient.