Multiple Choice
State the vertex, intercepts, and domain & range for each quadratic.
12. Quadratic Equations and Functions
Graphing Quadratic Equations
Multiple Choice
Graph the following quadratics and state its vertex and intercepts.
A
Vertex: , -intercept: ; -intercept: None
B
Vertex: , -intercept: None; -intercept:
C
Vertex: , -intercept: ; -intercept: None
D
Vertex: , -intercept: None; -intercept:
Verified step by step guidance1
Identify the quadratic equation given: \(y = 4x^2 - 8x + 5\).
Find the vertex using the vertex formula \(x = -\frac{b}{2a}\), where \(a = 4\) and \(b = -8\). Calculate \(x\) coordinate of the vertex.
Substitute the \(x\) value of the vertex back into the equation to find the \(y\) coordinate of the vertex.
Find the \(y\)-intercept by evaluating the function at \(x = 0\), which gives the point \((0, y)\).
Find the \(x\)-intercepts by solving the quadratic equation \(4x^2 - 8x + 5 = 0\) using the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\).
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